Consider whether you need to continue using your old name alongside your new one until clients are used to the new company name. For example, 'Atom Content Marketing (formerly BHP Information Solutions)'.

Consider using PR or blogging to publicise the name change. Will you tell some people confidentially ahead of the launch, to make them feel special?

Communicate the name change to staff, customers, suppliers, the authorities (where are you registered under your old name?) and other contacts.

Consider any other IT-related naming issues. For example, if you use a Virtual Private Network (VPN), update its name.

Switch email address from your old one to your new one, and change the contact details in your email signature.

Set up a website redirect from your old website to your new one.

Create a set of designs (logo, website, stationery, Twitter wallpaper, and so on) incorporating your new name. Consider using a freelance marketplace for this, eg Upwork or Peopleperhour.

Consider trademarking the new name.

Register the new name at Companies House if you are a limited company.

Register your new website url: consider registering other similar urls and establishing redirects to your main website.